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Roman Krzysztofowicz and Ashley A. Sigrest

Abstract

A comparative verification is reported of 2631 matched pairs of quantitative precipitation forecasts (QPFs) prepared daily from 1 October 1992 to 31 October 1996 by the Hydrometeorological Prediction Center (HPC) and the Weather Service Forecast Office in Pittsburgh (PIT). The predictand is the 24-h spatially averaged precipitation amount. The property of QPF being verified is calibration. Four interpretations of each QPF are hypothesized and verified: an exceedance fractile, a conditional exceedance fractile, the mean, and the conditional mean (with conditioning on precipitation occurrence).

Time series of calibration statistics support the following conclusions. (i) The HPC QPF, which lacks an official interpretation, is calibrated as the 18%–19% exceedance fractile and as the conditional median, on average. (ii) It serves as a useful guidance to local forecasters. (iii) Pittsburgh forecasters adjust the guidance in the correct direction to produce PIT QPF, whose official interpretation is the (unconditional) median. (iv) Relative to this interpretation, HPC QPF has a substantial overestimation bias, which hampers the calibration of PIT QPF. (v) The calibration of each QPF lacks consistency over time. (vi) To improve the potential for good calibration, the guidance QPF and the local QPF should be given the same probabilistic interpretation; the conditional median of the spatially averaged precipitation amount is recommended.

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Ashley A. Sigrest and Roman Krzysztofowicz

Abstract

The predictand of a probabilistic quantitative precipitation forecast (PQPF) may be either a point precipitation amount or a spatially averaged precipitation (SAP) amount. At the current state of the art, it is the SAP amount (the volume of water accumulated over an area during a period) that is most predictable. This case study compares the climatic PQPFs of the two predictands within a river basin in the Appalachians, then highlights similarities and distinctions of which the forecasters should be aware. Empirical relations reveal whether or not a given statistic of the point precipitation amount is (i) locally invariant, that is, does not vary appreciably within some area so that a single estimate (e.g., a spatial average) can approximate the statistic at every point within the area, and (ii) amenable to averaging, that is, can be averaged over some area to obtain an approximation to the statistic of the SAP amount. The study also illustrates the effect of elevation on the statistics of point precipitation and highlights seasonal differences. The conclusions point to a need for local climatic guidance to help forecasters in calibrating PQPFs.

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Roman Krzysztofowicz and Ashley A. Sigrest

Abstract

From 1 August 1990 to 31 July 1995, the Weather Service Forecast Office in Pittsburgh prepared 6159 probabilistic quantitative precipitation forecasts. Forecasts were made twice a day for 24-h periods beginning at 0000 and 1200 UTC for two river basins. This is the first in a series of articles devoted to a comprehensive verification of these forecasts. The property verified herein is calibration: a match between forecast probabilities and empirical frequencies of events.

Monthly time series of calibration statistics are analyzed to infer (i) trends in calibration over time, (ii) the forecasters’ skill in quantifying uncertainty, (iii) the adaptability of forecasters’ judgments to nonstationarities of the predictand, (iv) the possibility of reducing biases through dynamic recalibration, and (v) the potential for improving calibration through individualized training.

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Roman Krzysztofowicz and W. Britt Evans

Abstract

The Bayesian processor of forecast (BPF) is developed for a continuous predictand. Its purpose is to process a deterministic forecast (a point estimate of the predictand) into a probabilistic forecast (a distribution function, a density function, and a quantile function). The quantification of uncertainty is accomplished via Bayes theorem by extracting and fusing two kinds of information from two different sources: (i) a long sample of the predictand from the National Climatic Data Center, and (ii) a short sample of the official National Weather Service forecast from the National Digital Forecast Database. The official forecast is deterministic and hence deficient: it contains no information about uncertainty. The BPF remedies this deficiency by outputting the complete and well-calibrated characterization of uncertainty needed by decision makers and information providers. The BPF comes furnished with (i) the meta-Gaussian model, which fits meteorological data well as it allows all forms of marginal distribution functions, and nonlinear and heteroscedastic dependence structures, and (ii) the statistical procedures for estimation of parameters from asymmetric samples and for coping with nonstationarities in the predictand and the forecast due to the annual cycle and the lead time. A comprehensive illustration of the BPF is reported for forecasts of the daily maximum temperature issued with lead times of 1, 4, and 7 days for three stations in two seasons (cool and warm).

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Roman Krzysztofowicz, William J. Drzal, Theresa Rossi Drake, James C. Weyman, and Louis A. Giordano

Abstract

A methodology has been formulated to aid a field forecaster in preparing probabilistic quantitative precipitation forecasts (QPFs) for river basins. The format of probabilistic QPF is designed to meet three requirements: (i) it is compatible with the forecaster's judgmental process, which involves meteorologic inference and probabilistic reasoning; (ii) it can be input directly into a hydrologic model that produces river stage forecasts (at present); and (iii) it provides information sufficient for producing probabilistic river stage forecasts (in the future).

The methodology, implemented as a human–computer system, has been tested operationally on two river basins by the Weather Service Forecast Office in Pittsburgh, Pennsylvania, since August 1990. The article elaborates on the rationale behind methods being proposed, details system components, recommends an information processing scheme for judgmental probabilistic forecasting, and outlines training, testing, and verification programs.

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